Variance: Why we use the squared deviation instead of absolute deviation

This is my attempt to explain why we use squared deviation instead of absolute deviation to calculate variance. Spoiler alert! I have no good reason...

[@bernhardkoster3095]

Naming Fisher is ok, but the deeper reason, why we use ^2 is as always in math the little giant Carl Friedrich Gauss. He wanted to estimate from data the most probable point in the sky where he could redisdover Ceres, a small planet. Doing this, he found, that ^2-deviation is a very useful number (think of the density of the normal distribution, which we find everywhere in the nature and of course the central limit theorem!). But anyhow, you always have to look at your problem, what is a useful measure of deviation. This could also be MAD (Laplace-Distribution) or ^4 (Kurtosis) or ... which sometimes describes finance data better or more deeply than using only ^2. Or take in statistics the method of general moments, where we more or less say, let`s look on the data take ^n and than we empirically see, which n fits best the data. Essential point: Only because almost everybody uses ^2, this is not always the proper measure

[@heyitspranav]

Your video heading was intended to explain the rationale behind square while you spend 99% of the time explaining how variance is calculated....and not enough reason for why square was applied....shame on you....rubbish video !!!

[@kxrlzzz795]

Thanks for letting us know! Just watched through another one that did the same exact thing.

[@giorgiosnello4167]

In the end you didn't explain why we used sqaured deviation. Please change the title of your video.

[@andrewjustin256]

That was exactly what I had been waiting for and in the end I got to know, quote unquote "there are a whole lot other reasons and we'll get to them next time".

[@stonwall9065]

The short answer is, it's arbitrary. Created, like all math. That said, there is reason for it. He references some at the end, but otherwise is demonstrating what the ^2 does mathematically instead of absolute value. Not a "deep" video, but I got my answer actually. So thanks.

[@marcoglara2012]

Thanks for the honesty. Seriously. Most teachers just try to give me BS reasons and it’s annoying.

[@tianyiyin4847]

What does BS mean?

[@chrisbrolin5122]

@@tianyiyin4847 bullshit

[@marcoglara2012]

Thank you. Everyone else has been giving me BS answers like “absolute value is hard to undo”. nonsense like that. I expected it was something like this. Thank you for the honesty.

[@dhrubajyotipaul8204]

Haha. Those ppl don't get that square and square root is essentially an absolute value xD

[@joyanbhathena7251]

So standard deviation penalizes the outliers more than the mean absolute deviation. Thanks for making this video!

[@dhrubajyotipaul8204]

No. Absolute Deviation is not the same as standard deviation. Standard Deviation is the square root of the variance. Absolute deviation is the average of all the residuals. Notice that you do NOT get the variable is you square the absolute deviation.

[@dudana53]

it's no help

[@janm20]

Answer to the question is at 12:39. ;-) Thanks for the useful video!

[@hinahbashir]

It penalizes the outliers bt how by giving them extra weights and incorporating them in the model

[@nneisler]

And here I was looking for an actual answer, not a hint for another video.

[@mehmetkaya4330]

But how is it punished? And why punish? I mean how does it help?

[@logantate3269]

I wish he would have continued on to show the standard deviation and the mean absolute deviation. The standard deviation is always bigger than the mean absolute deviation because bigger numbers "count more" in mean squared deviations than they do in mean absolute deviations. So it "punishes" larger values (not even necessarily outliers but especially outliers) by giving them extra influence on raising that standard deviation value. The idea of that being "punishment" is what he refers to as "golf scoring" because a higher standard deviation is "bad." I don't like the use of the word "punish" here because it's not a neutral word, but that's what he means. [I know you asked this question years ago, but in case someone sees it and has the same question, I wanted to help!]

[@saraimarte]

@@logantate3269 thanks!

[@Sprajt]

I have to gently agree with others here. I like the video, but it fails to explain why standard deviation is being used over the MAD. Good video - misleading title.

[@frankt9156]

Ok this is a total click bait. Make me mad a little bit. This should be re title as What is variance.

[@fixedshot]

The simple answer is because I told you so? oh my

[@tianhouzhang6492]

please punish me! oh~yes~

[@johanroypaul2816]

Dear sir , why did you use the word "around " while defining Variance ? (Variance is howmuch a population varies 'around 'the mean) why not use 'from' the mean?

[@logantate3269]

I think "around" is used because of the mean being in the middle somewhere and values deviating above (to the right) and below (to the left). I think "from" is also fine for "deviation from the mean." I don't think people generally say "variance from the mean," but if you used this phrasing probably everyone would understand you anyway.

[@johanroypaul2816]

@@logantate3269 Thank you very much sir

[@sanjitgera1160]

the reliebility of this video comes from the use of a sharpie

[@sanjitgera1160]

i watch the whole video, but what do i get, "linear regression and all other skew of reasons"

[@sagemaster3408]

Subscribed just because of bellyrubs😊

[@natemarsden7638]

Incorrectly titled. Very helpful if teaching standard deviation but a complete waste of time if you are actually trying to figure out the answer to the titles question. “Because I said so”....?? Lol.... This is why people are afraid of math.

[@canadacanada7788]

I'll tell you why if you go with me

[@jaidebmandal2809]

Just now wasted my 13.44 mins

[@Rey_B]

didn't get my answer but it was nice

[@just_for_fun1711]

So the title of is a question that u suppose to answer it and explain it , but all you said is "a guy said so " , that by one of the useless video I watched